The document discusses the kineto-elasto dynamic analysis of the Puma-560 robot manipulator, emphasizing the need for lightweight designs to enhance speed and performance while addressing the complexities of dynamic control due to structural flexibility. It outlines the derivation of motion equations based on a distributed parameter method, the use of finite element analysis (FEA) for elastic deformation modeling, and various computational approaches implemented in MATLAB. The findings aim to improve trajectory accuracy and efficiency through elastic compensation in robotic programming.

1. IOSR Journal of Mechanical and Civil Engineering (IOSR-JMCE)
e-ISSN: 2278-1684,p-ISSN: 2320-334X, Volume 8, Issue 3 (Sep. - Oct. 2013), PP 33-40
www.iosrjournals.org
www.iosrjournals.org 33 | Page
Kineto-Elasto Dynamic Analysis of Robot Manipulator Puma-560
D. Pratap, Dr. Y. V. Mohan Reddy
1 ( Mechanical Engineerig,G.Pulla Reddy Engineerig College (Autonomous) /J Ntu Anantapur , India)
2 (Mechanical Engineerig,G.Pulla Reddy Engineerig College (Autonomous) /J Ntu Anantapur , India )
Abstract: Current industrial robots are made very heavy to achieve high Stiffness
which increases the accuracy of their motion. However this heaviness limits the robot speed and in masses the
required energy to move the system. The requirement for higher speed and better system performance makes it
necessary to consider a new generation of light weight manipulators as an alternative to today's massive
inefficient ones. Light weight manipulators require Less energy to move and they have larger payload abilities
and more maneuverability. However due to the dynamic effects of structural flexibility, their control is much
more difficult. Therefore, there is a need to develop accurate dynamic models for design and control of such
systems.This project presents the flexibility and Kineto - Elasto dynamic analysis of robot manipulator
considering deflection. Based on the distributed parameter method, the generalized motion equations of robot
manipulator with flexible links are derived. The final formulation of the motion equations is used to model
general complex elastic manipulators with nonlinear rigid-body and elastic motion in dynamics and it can be
used in the flexibility analysis of robot manipulators and spatial mechanisms. Manipulator end-effector path
trajectory, velocity and accelerations are plotted. Joint torques is to be determined for each joint trajectory
(Dynamics) .Using joint torques, static loading due to link’s masses, masses at joints, and payload, the robot
arms elastic deformations are to be found by using ANSYS-12.0 software package. Elastic compensation is
inserted in coordinates of robotic programming to get exact end-effectors path. A comparison of paths
trajectory of the end-effector is to be plotted. Also variation of torques is plotted after considering elastic
compensation. These torque variations are included in the robotic programming for getting the accurate end-
effect or’s path trajectory.
Keywords: Manipulator, Speed, Accuracy,, Path trajectory, FEA analysis
I. Introduction
Machines are used in a variety of applications: pick-and-place operations, welding, machining, etc.
Such machines can be divided into two units. the physical mechanism composed of links and actuators, and the
control system. The number of actuators present in the mechanical system depends on the number of
independent machine axes, or degrees of freedom. For example, a typical articulated six degree of freedom
manipulator contains six rotating actuators. A five-axis high-speed CNC machining centre would contain three
linear actuators and two rotating actuators. A motion task given to the machine must ultimately be represented
as a reference signal, which is sent to the control system. The control system acts to make the machine track the
reference signal by activating the appropriate actuators. If the reference signal changes too quickly, given the
dynamic limitations of the machine, the tracking of the reference signal will be poor, regardless of the control
system design.
Computer algorithms are designed to calculate an appropriate reference signal based on the desired task
path and time-related limits (such as speed and acceleration). This reference signal is the trajectory, and can be
defined as a locus of points in operational or joint space on which a time-law has been specified. The generation
of an appropriate trajectory is the problem that is being investigated in this thesis .The path along which the
trajectory is defined can be point-to-point; namely, the machine is required to move between the two points but
is not given any fixed intermediate path. This type of path is useful in manipulator pick-and-place operations. A
path can also be completely specified through use of geometric functions. This type of path is commonly used in
CNC machining applications or in manipulator applications when obstacles are present, or when it is necessary
to ensure that the end effector follows as specific path.

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1.11 General Specifications
Performance:
Repeatability
± 0.004in. (±0.1mm)
Load capacity 5.5 lbs. (2.5 kg)
Straight line velocity 20 in/s max. (0.5 m/s max.)
II. Flow Chart
2.1 Problem Formulation
Flow chart
The main tasks of the project
III. Literature Survey
Numerous investigations have been carried out in the fields of Dynamics of flexible robot manipulator and its
deflections, velocity,acceleration,torque, variations and are described below
MOH.KHAIRUDIN in 2010 discussed about the modeling of a flexible link manipulator using
lagrangian technique in conjunction with the assumed mode method. A pay load is added to the tip of the outer
link, while hub inertias are included at the actuator joints. The lagrangian approach is used to derive the
dynamic model of the structure,the dynamic model of the flexible link manipulator verified using matlab. The

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emphasis has been set on obtaining accurate equation of motion that display the most relevant aspects of the
coupling between rigid and flexible dynamics.
A.AHMADI NADOOSHAN in 2008 discussed about the modeling and vibration of a flexible
link manipulator with tow flexible link and rigid joints are investigated which can include an arbitrary number
of flexible links. Hamilton principle and finite element approach is proposed to model the dynamics of flexible
manipulators the links are assumed to be deflection due to bending. The association between elastic
displacements of links is investigated, took in to the account the coupling effects of elastic motion and rigid
motion. The dynamic behaviour due to the flexibility of links is demonstrated through numerical
simulation.The rigid-body motion and elastic deformation are seperated by linearizing the equations of motion
around rigid body reference path. Simulation results are shown on for both position and force trajectory tracking
tasks in the presence of varying parameters. The proposed method can be used in both dynamic simulation and
controller design.
E. Abele in 2008 discussed about different implementations of elastic joint models of
industrial robots are described and compared established in ADAMS and SimMechanics. The models are
intended to be used for path prediction under process force load due to Roboforming and high speed cutting,
respectively. The computational results have been compared and showed good agreement. In experiments of
robot forming and robot milling the measured and simulated path deviations according to the process force are
compared. The experiments are descriped and the results are discussed within the paper as a basis of a next step
model based compensation of the path deviation.
Sinan Kilicaslan in 2009 proposed robot manipulators with flexible links, a new method is
proposed to control their constrained end-effectors motions and the associated contact forces and/or moments.
The equations of motion are separated into two parts that represent the pseudo static equilibrium and the
deviations from it. The feed forward part of the control input based on the pseudo static equilibrium is
determined algebraically and the feedback part of the control input for the stabilization of the deviations is
obtained by means of a state-variable feedback law using measurements of the contact forces and/or moments,
the strains in the links, the joint variables, and the end-effectors position and velocity. The feedback gain matrix
is determined online by a continuously updated pole placement process. The method is demonstrated by means
of a planar two-link robot with a flexible forearm which is constrained to move on a cylindrical surface.
Furthermore, in order to investigate the effects of the modeling discrepancies caused by using lower order
models, a “sub model controller” is designed using a model with only the first mode and it is applied to the same
system with the two-mode model.
IV. Matlab
4.1 Basics Of Matlabmatlab (matrix laboratory) is a numerical computing environment and fourth-generation
programming language. Developed by Math Works, MATLAB allows matrix manipulations, plotting
of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs
written in other languages, including C, C++, and Fortran.
Although MATLAB is intended primarily for numerical computing, an optional toolbox uses the symbolic
engine, allowing access to computing capabilities. An additional package, Simulink, adds graphical multi-
domain simulation and Model-Based Design for dynamic and embedded systems.
In 2004, MATLAB had around one million users across industry and academia. MATLAB users come from
various backgrounds of engineering, science, and economics. MATLAB is widely used in academic and
research institutions as well as industrial enterprises.
Vectors/Matrices
MATLAB is a "Matrix Laboratory", and as such it provides many convenient ways for creating
vectors, matrices, and multi-dimensional arrays. In the MATLAB vernacular, a vector refers to a one
dimensional (1×N or N×1) matrix, commonly referred to as an array in other programming languages.
A matrix generally refers to a 2-dimensional array, i.e. an m×n array where m and n are greater than or equal to
1. Arrays with more than two dimensions are referred to as multidimensional arrays.
Structures
MATLAB supports structure data types. Since all variables in MATLAB are arrays, a more adequate
name is "structure array", where each element of the array has the same field names. In addition, MATLAB
supports dynamic field names (field look-ups by name, field manipulations etc). Unfortunately, MATLAB JIT
does not support MATLAB structures, therefore just a simple bundling of various variables into a structure will
come at a cost.

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Function Handles
MATLAB supports elements of lambda-calculus by introducing function handles, or function
references, which are implemented either in .m files or anonymous/nested functions.
Secondary Programming
MATLAB also carries secondary programming which incorporates the MATLAB standard code into a
more user friendly way to represent a function or system.
Classes
MATLAB supports classes, however the syntax and calling conventions are significantly different than
in other languages, because MATLAB does not have reference data types. For example, a call to a method
objects. Method (); cannot normally alter any variables of object variable. To create an impression that the
method alters the state of variable, MATLAB toolboxes use evalin () command, which has its own restrictions.
Object Oriented Programming
MATLAB's support for object-oriented programming includes classes, inheritance, virtual dispatch,
packages, pass-by-value semantics, and pass-by-reference semantics.
Interfacing With Other Languages
MATLAB can call functions and subroutines written in the C programming language or FORTRAN. A
wrapper function is created allowing MATLAB data types to be passed and returned.
Elastic compensation co-ordinates
10
0.4200
0.18
0.1800
23.1986
-126.08
141.960
9
0.3844
0.18
0.1767
25.0894
-132.72
152.752
8
0.3489
0.18
0.1733
27.290
-138.23
161.870
7
0.3133
0.18
0.1700
29.876
-142.77
169.474
6
0.2778
0.18
0.1667
32.9432
-146.48
175.700
5
0.2422
0.18
0.1633
36.616
-149.52
180.679
4
0.2067
0.18
0.1600
41.054
-152.07
184.546
3
0.1711
0.18
0.1567
46.50
-154.28
187.44
2

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2
0.1356
0.18
0.1533
53.018
-156.28
189.50
2
1
0.10
0.18
0.15
60.945
4
-158.13
190.85
1
S.No
X(M)
Y(M)
Z(M)
θ1(Deg)
θ2(Deg)
θ3(Deg)
Table 4.1.1 co-ordinates
4.2 Mat lab program
m2 = 40; m = mass (kg)
m3 = 14.5; L = length (m)
m23 = 2.5; G = gravity (m/s2
)
m34 = 5; T = time (sec)
L2 = 0.432;
L3 =0.432;
Ma = 0.5*m2+ m23 + m3 + m34; Ic = (m3+4*m34)*L3^2; Ia = (0.25*m2+m23+m3+m34)*L2^2;
G = 10; Ib = (m3+2*m34)*L2*L3; T = 0:0.01:5; Mb = m3+2*m34;
4.3 Linear Order Equation For Base
Fig.1 Base Rotation Fig.2 Base Angular Velocity
Fig.3 Base Torque

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V. Fea Analysis
ANSYS Ver. XI is used for finite element Analysis of the Robot Manipulator
5.1 Element types:
5.1.1 BEAM188 Element Description
3-D Linear Finite Strain Beam: BEAM188 is suitable for analyzing slender to moderately
stubby/thick beam structures. This element is based on Timoshenko beam theory. Shear deformation effects are
included.
BEAM188 is a linear (2-node) or a quadratic beam element in 3-D. BEAM188 has six or seven degrees
of freedom at each node, with the number of degrees of freedom depending on the value of KEYOPT(1). When
KEYOPT (1) = 0 (the default), six degrees of freedom occur at each node. These include translations in the x, y,
and z directions and rotations about the x, y, and z directions. When KEYOPT (1) = 1, a seventh degree of
freedom (warping magnitude) is also considered. This element is well-suited for linear, large rotation, and/or
large strain nonlinear application
5.2 Graphical user interface process
a) Preferences > structural
b) Element type>Add
1. BEAM- 188
2. MPC184 REVOLUTE JOINT
a) Real constants
For BEAM- 188
1. Link1
Ri = 0.0331m
Ro = 0.0496 m
2. Link2
h = 0.189 m
b= 0.063 m
3. Link3
h = 0.189 m
b= 0.063 m
d) Material properties
Young’s Modulus=2e11 N/m2
Density=7800 kg/m3
Poisson’s ratio=0.3
e) FE Model
create > (Node 1)
(Node 2, 3)
(Node 4, 5)
(Node 6)
Boundary conditions (Degrees of Freedom)At node 1 : All degrees of freedom fixed
At node 2 & 3: UX, UY, UZ, ROTX and ROTY=0

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At node 4 & 5: Revolute joint
Loading conditions
Position Joint torque at node 2
(MZ in Nm)
Joint torque at
node 4 (MZ in Nm)
Mass atjoint
(atnode4)
(in Nm)
Mass at joint (at
node 6)
(in Nm)
1 172.6 -183.9 -25 -50
2 167 -107 -25 -50
3 162.4 -51.23 -25 -50
4 155.3 -14.8 -25 -50
5 139.2 10.7 -25 -50
Table 5.2.1 loading conditions
Processing Solution ctrls > ok
Solve > current L.S > ok
Post processing
a) List of Displacements
Table 5.2.2 List of Displacements
5.3 .1Deformed shape
Figure 5.3.1 Deformed shape Figure 5.3.2 Position 1
Figure 5.3.3 Position 2
Figure 5.3.4 Position 3
SL.No Ux (in m) Uz (in m)
1 -0.4953*10-4
-0.36103*10-4
2 -0.55871*10-5
-0.10547*10-4
3 -0.34072*10-3
-0.60530*10-2

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VI. Comparative results
Fig.1 Angular Velocity Fig.2 Angular Acceleration
Fig.3 Base Torque
VII. Conclusion
This project presented the Kineto-Elasto dynamic analysis of robot manipulator. The end-effectors
holding an object and passing through a considered path trajectory, the co-ordinate positions of the end-effectors
is considered at ten positions. Inverse kinematic analysis has been performed for finding the corresponding link
positions. Dynamic analysis is performed to find the velocities, accelerations and joint torques for moving the
end-effectors in the considered path trajectory with the help of MATLAB-2008a software. Using joint torques,
static loading due to link’s masses, masses at joints, and payload, the Robot manipulator arms elastic
deformations are found by using ANSYS-12.0 software package. Elastic compensation inserted in the co-
ordinates of robotic programming to get exact end-effectors path. A comparison of path trajectories and
variation of torques is plotted after considering elastic compensation. It is suggested that by compensating the
joints torque variations in the robotic programming, the trajectory path of the end-effectors will be accurate than
the specified repeatability of ±0.1 mm in the manual of PUMA-560.
7.1 Future Scope
1 The robotic programming language can be modified and that can be incorporated and tested with puma robot
for getting accurate path trajectory of the end effectors according to the result obtained in this theses work.
2. This analysis may be further extended by considering the inertia effect due to the speed increased in the
robot arm. Feed back control for position, velocity and acceleration can be incorporated in the analysis.
References
[l] Moh.khairudin, “Dynamic modeling of a flexible link manipulator robot “university negeri, Yogyakarta, Indonesia.2010 ISSN
1693-6930.
[2] A.Ahmadi nadooshan, E.Abedi, s.salehi,”Dynamic modeling of two flexible link manipulator”,2008International journal of aero
space and mechanical engineering.
[3] B.Subudhi, A.S morris “Dynamic modeling,simulation and controling of a manipulator with flexible links and
joints”,2008Robotics and atonomous systems.257-270.
[4] K.S. Fu, R.C. Gonzalez, and C.S.G. Lee, Robotics Control, Sensing, h i o n , and Intelligence,;McGraw-Hill, 1987.